Statistical Approach to Fuzzy Cognitive Maps

Fuzzy cognitive maps are studied from statistical standpoint. An analogy between these maps and linear regression and logistic regression models is drawn. Practical examples are also provided.Peer reviewe

Uncertainty Measurement for the Interval Type-2 Fuzzy Set

In this paper, two measures of uncertainty for interval type-2 fuzzy sets are presented, evaluated, compared and contrasted. Wu and Mendel regard the length of the type-reduced set as a measure of the uncertainty in an interval set. Green eld and John argue that the volume under the surface of the type-2 fuzzy set is a measure of the uncertainty relating to the set. For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give di erent results, there is considerable commonality between them. The concept of invariance under vertical translation is introduced; the uncertainty measure of a fuzzy set has the property of invariance under vertical translation if the value it generates remains constant under any vertical translation of the fuzzy set. It is left unresolved whether invariance under vertical translation is an essential property of a type-2 uncertainty measure

Ethical Issues in Engineering Models: An Operations Researcher’s Reflections

This article starts with an overview of the author’s personal involvement—as an Operations Research consultant—in several engineering case-studies that may raise ethical questions; e.g., case-studies on nuclear waste, water management, sustainable ecology, military tactics, and animal welfare. All these case studies employ computer simulation models. In general, models are meant to solve practical problems, which may have ethical implications for the various stakeholders; namely, the modelers, the clients, and the public at large. The article further presents an overview of codes of ethics in a variety of disciples. It discusses the role of mathematical models, focusing on the validation of these models’ assumptions. Documentation of these model assumptions needs special attention. Some ethical norms and values may be quantified through the model’s multiple performance measures, which might be optimized. The uncertainty about the validity of the model leads to risk or uncertainty analysis and to a search for robust models. Ethical questions may be pressing in military models, including war games. However, computer games and the related experimental economics may also provide a special tool to study ethical issues. Finally, the article briefly discusses whistleblowing. Its many references to publications and websites enable further study of ethical issues in modeling

A user-friendly earth system model of low complexity: the ESCIMO system dynamics model of global warming towards 2100

We have made a simple system dynamics model, ESCIMO (Earth System Climate Interpretable Model), which runs on a desktop computer in seconds and is able to reproduce the main output from more complex climate models. ESCIMO represents the main causal mechanisms at work in the Earth system and is able to reproduce the broad outline of climate history from 1850 to 2015. <br><br> We have run many simulations with ESCIMO to 2100 and beyond. In this paper we present the effects of introducing in 2015 six possible global policy interventions that cost around USD 1000 billion per year &ndash; around 1 % of world GDP. We tentatively conclude (a) that these policy interventions can at most reduce the global mean surface temperature &ndash; GMST &ndash; by up to 0.5 °C in 2050 and up to 1.0 °C in 2100 relative to no intervention. The exception is injection of aerosols into the stratosphere, which can reduce the GMST by more than 1.0 °C in a decade but creates other serious problems. We also conclude (b) that relatively cheap human intervention can keep global warming in this century below +2 °C relative to preindustrial times. Finally, we conclude (c) that run-away warming is unlikely to occur in this century but is likely to occur in the longer run. The ensuing warming is slow, however. In ESCIMO, it takes several hundred years to lift the GMST to +3 °C above preindustrial times through gradual self-reinforcing melting of the permafrost. <br><br> We call for research to test whether more complex climate models support our tentative conclusions from ESCIMO